We show here that a wide class of integral inequalities concerning functions on [0,1] can be obtained by purely combinatorial methods. More precisely, we obtain modulus of continuity or other high order norm estimates for functions satisfying conditions of the type ∫01∫01Ψf(x)-f(y)p(x-y)dxdy<∞ where Ψ(u) and p(u) are monotone increasing functions of |u|.

Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes